The image displays two functions, $f(x)$ (in red) and $g(x)$ (in blue), along with their corresponding graphs. The task is to find $(f \cdot g)(1)$, which refers to the product of the function values of $f(x)$ and $g(x)$ at $x = 1$.

To solve $(f \cdot g)(1)$:

1. Identify the values of $f(1)$ and $g(1)$ from the graph.
2. Multiply $f(1)$ by $g(1)$.

Let's break this down:

1. From the graph:

   • The value of $f(1)$ (red curve) at $x = 1$ is approximately 3.
   • The value of $g(1)$ (blue line) at $x = 1$ is approximately 2.

2. Now, compute $(f \cdot g)(1) = f(1) \cdot g(1)$: $(f \cdot g)(1) = 3 \cdot 2 = 6.$

Thus, $(f \cdot g)(1) = 6$.

Would you like any further details or clarifications on this problem?

Here are 5 related questions you might find helpful:

1. How do you determine the values of a function from a graph at specific points?
2. What does the notation $(f \cdot g)(x)$ represent in function operations?
3. Can the same procedure be used for any two functions $f(x)$ and $g(x)$?
4. What is the significance of finding the product of two functions at a specific point?
5. How can you find the intersection points of two graphs algebraically?

Tip: When dealing with function graphs, it's essential to read values accurately from the axes, especially at key points like intersections and specified $x$-values.